The existence of the Haar measure is a beautiful result that has a lot of applications. For example, one can prove using the Haar measure that the category of representations of a compact Lie group is semi-simple. Do you know any other nice applications of the Haar measure?
2026-04-03 12:44:27.1775220267
Nice applications of the Haar measure
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One important "application" is Peter-Weyl theorem. A good article can be found at here.